The routine reduces the target of M by elementary moves (see elementary) involving just d+1 variables. The outcome is probabalistic, but if the routine fails, it gives an error message.
i1 : kk=ZZ/32003 o1 = kk o1 : QuotientRing |
i2 : S=kk[a..e] o2 = S o2 : PolynomialRing |
i3 : i=ideal(a^2,b^3,c^4, d^5)
2 3 4 5
o3 = ideal (a , b , c , d )
o3 : Ideal of S
|
i4 : F=res i
1 4 6 4 1
o4 = S <-- S <-- S <-- S <-- S <-- 0
0 1 2 3 4 5
o4 : ChainComplex
|
i5 : f=F.dd_3
o5 = {5} | c4 d5 0 0 |
{6} | -b3 0 d5 0 |
{7} | a2 0 0 d5 |
{7} | 0 -b3 -c4 0 |
{8} | 0 a2 0 -c4 |
{9} | 0 0 a2 b3 |
6 4
o5 : Matrix S <--- S
|
i6 : EG = evansGriffith(f,2) -- notice that we have a matrix with one less row, as described in elementary, and the target module rank is one less.
o6 = {5} | c4 d5 0
{6} | -b3 0 d5
{7} | 0 -b3 -991a4-15744a3b+14712a2b2-5172a3c+5891a2bc-11967a2c2-c4
{7} | a2 0 -6544a4-14524a3b+13900a2b2-3414a3c-15853a2bc+13657a2c2
{8} | 0 a2 -5252a3-5281a2b+3445a2c
------------------------------------------------------------------------
0 |
0 |
-991a2b3-15744ab4+14712b5-5172ab3c+5891b4c-11967b3c2 |
-6544a2b3-14524ab4+13900b5-3414ab3c-15853b4c+13657b3c2+d5 |
-5252ab3-5281b4+3445b3c-c4 |
5 4
o6 : Matrix S <--- S
|
i7 : isSyzygy(coker EG,2) o7 = true |